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Theorem 3jaoian 1293
Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)
Hypotheses
Ref Expression
3jaoian.1  |-  ( (
ph  /\  ps )  ->  ch )
3jaoian.2  |-  ( ( th  /\  ps )  ->  ch )
3jaoian.3  |-  ( ( ta  /\  ps )  ->  ch )
Assertion
Ref Expression
3jaoian  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )

Proof of Theorem 3jaoian
StepHypRef Expression
1 3jaoian.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 434 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 3jaoian.2 . . . 4  |-  ( ( th  /\  ps )  ->  ch )
43ex 434 . . 3  |-  ( th 
->  ( ps  ->  ch ) )
5 3jaoian.3 . . . 4  |-  ( ( ta  /\  ps )  ->  ch )
65ex 434 . . 3  |-  ( ta 
->  ( ps  ->  ch ) )
72, 4, 63jaoi 1291 . 2  |-  ( (
ph  \/  th  \/  ta )  ->  ( ps  ->  ch ) )
87imp 429 1  |-  ( ( ( ph  \/  th  \/  ta )  /\  ps )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    \/ w3o 972
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975
This theorem is referenced by:  xrltnsym  11368  xrlttri  11370  xrlttr  11371  qbtwnxr  11424  xltnegi  11440  xaddcom  11462  xnegdi  11465  xaddeq0  27730  3ccased  29314
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